A simpler method to obtain a PTAs for connected k-path vertex cover in unit disk graph

Abstract

Given a connected graph G = (V, E), a connected k-path vertex cover (CVCPk) is a vertex set C ⊆ V which contains at least one vertex from every path of G on k vertices and the subgraph of G induced by C is connected. This paper presents a new PTAS for Min-CVCPkon unit disk graphs. Compared with previous PTAS given by Liu et al., Our method not only simplifies the algorithm but also simplifies the analysis by a large amount.